Diesel Combustion Modeling and Simulation
for Torque Estimation and Parameter
Optimization
Master’s thesisperformed in Vehicular Systems by
Fredrik Jones, Christoffer Jezek Reg nr: LiTH-ISY-EX -- 08/4072 -- SE
Presentationsdatum 2008-05-29
Publiceringsdatum 2008-06-11
Institution och avdelning Institutionen för systemteknik Department of Electrical Engineering
Språk Svenska
X Annat (ange nedan)
Engelska Antal sidor 54 Typ av publikation Licentiatavhandling X Examensarbete C-uppsats D-uppsats Rapport
Annat (ange nedan)
ISBN (licentiatavhandling) ISRN 08/4072
Serietitel (licentiatavhandling)
Serienummer/ISSN (licentiatavhandling)
URL för elektronisk version
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-12117 Publikationens titel
Diesel Combustion Modeling and Simulation for Torque Estimation and Parameter Optimization. Författare
Christoffer Jezek & Fredrik Jones Abstract
The current interest regarding how to stop the global warming has put focus on the automobile industry and forced them to produce vehicles/engines that are more environmental friendly. This has led to the development of increasingly complex controlsystem of the engines. The introduction of common-rail systems in regular automotives increased the demand of physical models that in an accurate way can describe the complex cycle within the combustion chamber. With these models implemented it is possible to test new strategies on engine steering in a cost- and time efficient way.
The main purpose with this report is to, build our own model based on
the existing theoretical models in diesel engine combustion. The model has then been evaluated in a simulation environment using Matlab/Simulink. The model that has been implemented is a multi-zone type and is able to handle multiple injections.
The model that this thesis results in can in a good way predict both pressure and torque generated in the
cylinder. More investigation in how the parameter settings behave in other work-points must be done to enhance the models accuracy. There is also some work left to do in the validation of the model but to make this possible more experimental data must be accessible.
Nyckelord
Diesel Combustion Modeling and Simulation
for Torque Estimation and Parameter
Optimization
Master’s thesisperformed in Vehicular Systems, Dept. of Electrical Engineering
at Link¨opings universitet by Fredrik Jones, Christoffer Jezek
Reg nr: LiTH-ISY-EX -- 08/4072 -- SE
Supervisor: Per ¨Oberg
Link¨opings Universitet Richard Backman
GM Powertrain Sweden AB Examiner: Associate Professor Lars Eriksson
Link¨opings Universitet Link¨oping, June 11, 2008
Abstract
The current interest regarding how to stop the global warming has put focus on the automobile industry and forced them to produce vehicles/engines that are more environmental friendly. This has led to the development of increas-ingly complex controlsystem of the engines. The introduction of common-rail systems in regular automotives increased the demand of physical models that in an accurate way can describe the complex cycle within the combustion chamber. With these models implemented it is possible to test new strategies on engine steering in a cost- and time efficient way.
The main purpose with this report is to, build our own model based on the existing theoretical models in diesel engine combustion. The model has then been evaluated in a simulation environment using Matlab/Simulink. The model that has been implemented is a multi-zone type and is able to handle multiple injections.
The model that this thesis results in can in a good way predict both pres-sure and torque generated in the cylinder. More investigation in how the parameter settings behave in other work-points must be done to enhance the models accuracy. There is also some work left to do in the validation of the model but to make this possible more experimental data must be accessible.
Sammanfattning
Dagens intresse av att hejda den globala uppv¨armingen har satt fokus p˚a att minska br¨anslef¨orbrukningen och utsl¨app fr˚an alla fordon som drivs av fos-sila br¨anslen. Ett steg i denna utveckling har gjort att styrningen av motorer blir mer och mer avancerade. I och med introduktionen av common-rail sys-tem f¨or dieselmotorer har efterfr˚agan ¨okat av fysikaliska modeller som p˚a ett korrekt s¨att kan beskriva det komplexa f¨orloppet som sker i f¨orbr¨anningskam-maren. Dessa modeller g¨or det m¨ojligt att p˚a ett kostnads- och tidseffektivt s¨att testa nya strategier p˚a motorstyrningen.
Huvudsyftet med denna rapport ¨ar att med hj¨alp av befintliga teoretiska modeller f¨or dieself¨orbr¨anning bygga upp en egen modell som baseras p˚a dessa. Denna modell har sedan utv¨arderats i en simuleringsbar milj¨o och f¨or detta ¨andam˚al har Matlab/Simulink anv¨ants. Modellen som har implementer-ats ¨ar av multizons-typ och klarar av att hantera multipla injektioner.
Den modell som denna rapport leder till kan p˚a ett bra s¨att skatta tryck och moment givet de m¨atdata som fanns tillg¨angliga. Det som beh¨ovs f¨orb¨attras med modellen ¨ar att unders¨oka hur parameters¨attningen st¨ammer vid flera olika arbetspunkter. Det kr¨avs ¨aven vidare arbete med verifiering av de olika parametrarna men f¨or att detta skall kunna genomf¨oras kr¨avs mer experiment-data.
Keywords: Multi-Zone, Diesel Combustion Modeling, Simulation for Torque Estimation, Parameter Optimization
Preface
This Master´s thesis has been performed at Link¨opings Tekniska h¨ogskola in collaboration with General Motors Powertrain (GM) during fall 2007. At GM’s request the thesis is based on a report made at the University of Salerno [2] presented at the SAE conference in 2005.
Objectives
The main objective with this thesis is to achieve a simulation model that sim-ulates the pressure trace in the cylinder during a compression/combustion cy-cle. From the pressure trace the torque that is produced can be calculated. The computer model should be implemented in MATLAB/Simulink and must be able to handle multiple injections.
Limitations
In this thesis there exists areas that not have been considered:
• the swirl factor. For different geometry of the piston there will be
dif-ferent swirl factors.
• that wall wetting may occur during the injection.
• that the cylinder wall temperature changes. This is considered to be
known.
• to evaluate the emissions that arise in the cylinder such as nitrogen
oxides and soot formation.
Another limitation is that this model must be initialized with correct initial condition such as inlet pressure and desired injection profile.
Thesis outline
Chapter 1 A short introduction of diesel engine and the combustion process. Chapter 2 Describes the theory behind diesel combustion in detail.
Chapter 3 Describes the choosen model approach and the implementation. Chapter 4 Explains the theory behind the implemented models.
Chapter 5 Gives a general view of the implementation. Chapter 6 Presents the validation of the models. Chapter 7 Presents results and conclusions.
Acknowledgment
We have some persons we would like express our gratitude to:
Without the help from our supervisor PhD student Per ¨Oberg this work would not been completed at all. The guidance he has given us and our countless dis-cussion has been invaluable. We also want to thank examiner Lars Eriksson at Link¨opings Universitet and Richard Backman at General Motors Powertrain. Last but not least we thank Caroline and Emma for proofreading the report.
Contents
Abstract iii
Preface and Acknowledgment iv
1 Introduction 1
2 Background 2
2.1 Diesel engine . . . 2
2.2 Diesel combustion . . . 3
2.3 Diesel oil . . . 5
3 The selected model 6 3.1 Model Structure . . . 6
3.1.1 Model approaches . . . 6
3.1.2 Implemented multi-zone model . . . 7
3.1.3 The zones . . . 7
3.1.4 Simulation of the model . . . 8
3.1.5 Initial conditions . . . 11
4 Theory behind the models 12 4.1 Thermodynamic model . . . 12
4.1.1 Implementation form of the equations . . . 13
4.2 Fuel injection model . . . 15
4.3 Fuel spray . . . 16
4.3.1 Fuel spray submodel . . . 17
4.4 Fuel evaporation submodel . . . 19
4.5 Combustion submodel . . . 19
4.6 Heat transfer submodel . . . 20
5 Implementation 22 5.1 General view . . . 22 5.2 Simulink . . . 22 5.3 S-functions . . . 23 5.4 Solver . . . 23 vii
5.5 psPack . . . 23
5.5.1 Thermal Properties . . . 24
6 Validation 25 6.1 Comments about the Validation . . . 25
6.2 Fuel injection . . . 25
6.3 Fuel spray validation . . . 26
6.4 Fuel evaporation model . . . 28
6.5 Evaporation and combustion submodel . . . 30
6.6 Heat transfer model . . . 32
6.7 Thermal properties . . . 33
6.8 Heat release analysis . . . 33
6.9 Pressure . . . 36
6.10 In-cylinder temperature . . . 37
7 Results and Conclusions 39 7.1 Results . . . 39
7.2 Conclusions . . . 40
7.3 Future work . . . 41
8 References 43 Notation 45 A Derivation of air entrainment rate and thermodynamic model 46 A.1 Air entrainment rate . . . 46
A.2 Thermodynamic Equations . . . 47
A.2.1 Energy at equilibrium . . . 47
A.2.2 Energy with a frozen mixture . . . 48
A.2.3 State equation - the ideal gas law . . . 49
B Sensitivity plots 50
Chapter 1
Introduction
After the introduction of common rail systems1, the interest of diesel engines
for automotive application has dramatically grown. A strong increase in fuel economy and significant reduction of emissions as well as combustion noise has been achieved, thanks to both optimized fuel strategies and improved fuel injection technology. The largest improvements have occurred in injection time response, injection pressure and nozzle characteristics. This has made it possible to use multiple injections (up to five or more) and has enhanced the fuel atomization. These improvements have resulted in a cleaner and more efficient combustion with benefits on emissions and fuel consumption. In order to increase the advantages due to the implementation of multiple in-jections on common rail diesel engines appropriate engine control strategies have to be developed. In this thesis a diesel engine combustion simulation model is developed that is based on the report Thermodynamic Modeling of
Jet formation and Combustion in Common Rail Multi-Jet Diesel Engines, see
[2]. This simulation model will make it possible to test and validate new injec-tion strategies instead of making expensive and time consuming experiments. The complexity of the combustion due to turbulent fuel-air mixing makes it difficult to make a model with high accuracy and low computational time; a trade-off has to be made between these two. Single zone models based on empirical heat release laws could be used to simulate SI2engine performance
and emissions but are inadequate to simulate the heterogeneous characteris-tics of the CI3 diesel combustion. In order to increase the accuracy in the
simulation, the approach in the implementation is to use a multi-zone model.
1Direct diesel injection, featuring high pressure injection with individual solenoid valves 2Spark Ignited
3Compression Ignited
Chapter 2
Background
This chapter is an introduction to the background theory of diesel engine and diesel combustion process.
2.1 Diesel engine
In mechanical terms, the internal construction of a diesel engine is similar to its gasoline counterpart-components e.g. pistons, connecting rods and a crankshaft are present in both. The different parts in the engine are shown in figure 2.1. Equal to a gasoline engine, a diesel engine operates in a four-stroke cycle (similar to the gasoline unit’s Otto cycle). The principal differences lie in the handling of air and fuel, and the method of ignition.[10]
A diesel engine relies upon compression ignition (CI) to burn its fuel, in-stead of the spark plug used in a gasoline engine. The compression phase can be seen in figure 2.1 B. If air is compressed to a high degree, its tempera-ture will increase to a point where fuel will burn upon contact with the air.[11] Unlike a gasoline engine, which draws a fuel-air mixture into the cylinder during the intake stroke, the diesel engine aspirates air alone. Figure 2.1 A shows how the air is inhaled into the cylinder during the intake phase. Fol-lowing intake, the cylinder is sealed as the intake valve is closed. The air charge is highly compressed to heat the charge to the temperature required for ignition. Whereas a gasoline engine’s compression ratio rarely is greater than 11:1 to avoid damaging preignition, a diesel engine’s compression ratio is usually between 16:1 and 25:1. This extremely high level of compression causes the air temperature to increase up to 700-900 degrees Celsius.[10] As the piston approaches top-dead-center (TDC), diesel-fuel oil is injected into the cylinder at high pressure, causing the fuel charge to be atomized. The
2.2. Diesel combustion 3
injection of diesel-fuel during the end of compression is illustrated in figure 2.1 B. As a result to the high air temperature in the cylinder, ignition instantly occurs, causing a rapid and considerable increase in cylinder temperature and pressure (generating the characteristic diesel ”knock”). The piston is driven downward with great force, pushing on the connecting rod and turning the crankshaft, as seen in figure 2.1 C.[10]
When the piston approach bottom-dead-center (BDC) the spent combustion gases are expelled from the cylinder to prepare for the next cycle. In figure 2.1 D it is shown that the exhaust valve is opened and the exhaust gases are ex-pelled. In many cases, the exhaust gases will be used to drive a turbocharger, which will increase the volume of the intake air charge. This results in a cleaner combustion and greater efficiency. Another use of the exhaust gas is to recycle it and mix it with the fresh air, called EGR1. This is another step to
decrease the emissions. [10], [11]
Another big difference between the diesel- and gasoline engine is that the diesel engine works with excess air and there exists no throttle. This results in a much lower pumping loss2and is a great advantage for the diesel engine.[1]
2.2 Diesel combustion
The essential features of the compression-ignition or diesel engine combus-tion process can be described as follows. Fuel is injected into the engine cylinder toward the end of compression stroke, just before the desired start of combustion. The fuel is injected at a very high velocity, due to the high pressure in the fuel injection system.[1]
The liquid fuel is usually injected as one or more jets through small orifices or nozzles in the injector tip, thereafter the fuel jet atomizes into small droplets and penetrates into the combustion chamber. The fuel vaporizes and mixes with the hot in-cylinder air. Since the air temperature and pressure are above the fuel’s ignition point, spontaneous ignition of parts of the mixed fuel and air occurs after a delay on just a few crank angle degrees. This is a phenom-ena of stratified combustion. [1]
The cylinder pressure increases rapidly as combustion of the fuel-air mixture occurs. The consequent compression of the unburned parts shortens the delay before ignition of the fuel and air, which has been mixed within combustible limits, that then burns rapidly. The increasing temperature and pressure also reduces the evaporation time of the remaining liquid fuel. Injection continues until the desired amount of diesel-fuel has entered the cylinder.[4]
1Exhaust Gas Recycling 2I.e energy loss.
4 Chapter 2. Background
A B
C D
Figure 2.1: The different phases of a four stroke diesel engine.
The steep pressure rise, that orginate from the ignition of the premixed fuel-air vapors is the source of the characteristic diesel engine combustion sound also known as knock. To prevent this steep pressure rise (knock) from oc-curring and to keep oxides of nitrogen (N Ox) emissions low a technique
with small pinjections before the main injection is often used. This re-sults in a smother rise in cylinder pressure, which reduces the noise. Another result is that the global temperature is decreased which lowers the (N Ox)
emissions.[1], [2]
Another possibility is to use injections after the main injection i.e. post-injection. The main idea with this post-injection is to reduce foremost the
2.3. Diesel oil 5
soot but also (N Ox) due to a second burn of the incomplete combusted gas.
In figure 2.2 a typical injection profile with both pre- and post-injections is presented. [4] Injec tion r a te Time Pre-injection Main injection Post-injection
Figure 2.2: Principle of a typical multiple injections.
2.3 Diesel oil
In an engine point of view, the important characteristics in diesel oils appear to be ignition quality, density, heat of combustion, volatility, cleanliness and noncorrosiveness. As density and heat of combustion depend almost entirely on molecular weight it is impossible to secure appreciable departures from these two qualities as they are strongly correlated. With a given density the volatility, viscosity and ignition delay (cetan number) tend to change together. This is becuase they are all sensitive to molecular arrengement as well as to molecular size. All these relationships makes it very difficult to determine how one of these qualities alone effects the engine performance.[7]
The term ignition quality, loosely cover the ignition-temperature-versus-delay characteristics of a fuel when used in an engine. At a given speed, compres-sion ratio, air inlet and jacket temperature, a good ignition quality means a short delay angle. Effects of the ignition quality in engine performance is the improvement in cold-starting characteristics and engine roughness. The engine roughness applies to the intensity if vibration of various engine parts caused by high rates of pressure rise in the cylinders.[7]
Chapter 3
The selected model
This chapter presents the model approach and which assumptions that have been made.
3.1 Model Structure
Due to the complexity of the diesel engine combustion and the turbulent fuel-air-mixing it is hard to develop a model that is accurate enough but that does not have too long computational time. There exists different approaches to implement a diesel combustion model i.e. single-zone, zone and multi-dimensional. To get an model that is accurate enough, has a acceptable sim-ulation time and has a complexity level that reflects the timeframe of this thesis, a multi-zone model has been selected. [4]
3.1.1 Model approaches
The different model approaches can be summarized as followed:
• Single-zone. A single-zone model is often used if there exists a need to
have a fast and preliminary analysis of the engine performance. Single-zone models assume that the cylinder charge is uniform in both com-position and temperature, at all time during the cycle. This approach is often used when simulation is made of a gasoline engine due to the homogeneous combustion. To use a single-zone model in the diesel case the model must be based on empirical heat-release laws. This ap-proach need a wide identification analysis. Therefore is this apap-proach excluded in this thesis. [4]
• Multi-dimensional. A multi-dimensional model, resolve the space of
the cylinder on a fine grid, thus providing a great amount of special information. This approach has its downside in computational time
3.1. Model Structure 7
and need of storage space. Therefore this approach is also excluded in our thesis. [4]
• Multi-zone. As an intermediate step between single-zone and
multi-dimensional models, multi-zone models can be effectively used to model diesel engine combustion systems. Selecting the multi-zone approach the advantages of single- and multidimensional models can be com-bined. By implementing a multi-zone model all the information needed is obtained in a reasonable time. The information given by the model is sufficient to achieve the thesis objectives. Therefore this approach is used in this thesis. [4]
3.1.2 Implemented multi-zone model
The multi-zone selected is based on the article Thermodynamic modeling of
jet formation and combustion in common rail multijet diesel engines and is
able to handle multiple injections. The article presents model for the fuel evaporation, air entrainment and combustion. The presented models for fuel evaporation and combustion is based on semi empirical expressions that only considers a mass rate.[2]
An analytical thermodynamical model is also presented but is not used in this thesis. In the package psPack1there exists a thermodynamical solver that
handle multiple zones and therfore is this solver used instead. A fuel injection model has to be implemented from another source due to lack of that kind of model in [2]. These models will all be submodels in the entire model. There will be communiction between the submodels and together these submodels will work as a unit. Figure 3.1 shows a hierarchy view of how the entire model is built and in figure 3.2 it is shown a flowchart over the different submodels that is implemented and how they interact with the thermodynamical model.
3.1.3 The zones
The multi-zone model is divided in the following zones: liquid-zone (l), air-zone (a), prepared-air-zone (p) and burned-air-zone (b). All diesel-fuel that’s in a liquid state is placed in the liquid-zone. The liquid-zone is seen as an incom-pressible liquid and is therefore excluded from the thermodynamic model. The liquid zone will only occupy a known volume in the combustion cham-ber. When the injected diesel-fuel vaporizes due to heat and high pressure it transfers to the prepared-zone. All fresh air, i.e. air that is not yet burned, is placed in the air-zone. When the fresh air and the vaporized fuel react (burns) the burned gas transfers to the burned-zone.
8 Chapter 3. The selected model
Entire model
inital conditions torque estimation
Layer 1
Submodel 1
internal signals internal signals
Submodel 2
internal signals internal signals
Submodel 3
internal signals internal signals
Layer 2
Layer 3
Equation 1
internal signals internal signals
Equation 2
internal signals internal signals
Equation 3
internal signals internal signals
Figure 3.1: Hierarchy view of the models.
Fuel Injection System
Fuel Spray Submodel
Evaporation Submodel
Combustion Submodel
Thermodynamic Model
p,T p,T
Figure 3.2: Flowchart over the implemented submodels.
3.1.4 Simulation of the model
To implement the model in a simulation environment the simulation process is divided into two steps.
3.1. Model Structure 9
• Step 1 Step one (compression) occurs immediately after IVC2and no
injection of fuel has jet been done. Therefore there only exists fresh air, EGR and in-cylinder residual gas. This gas composition is considered as a fully mixed homogenous gas with the same pressure and tempera-ture in the whole cylinder. This is illustrated in figure 3.3. In this step the simulation uses the following states:
States(step1) =¡ pglobal Vglobal Tglobal
¢
(3.1)
Figure 3.3: Compression with the homogeneous gas with air, egr and
residual-gas.
• Step 2 After the compression phase (step 1) comes the combustion
phase (step 2). In step two the fuel injection system is activated. At this point the cylinder is devided in four different zones. For each one of the simulated zones are also the unique thermal properties calculated. This results in following continuous states when simulating step 2:
States(step2) =¡ pglobal Va Ta Vp Tp Vb Tb
¢ (3.2) Where a stands f¨or air, p for prepared and b for burned.
The liquid-zone consists of the injected fuel, the air-zone consists of fresh air, the prepared-zone consists of vaporized fuel and the
burned-zone of combusted gas. Figure 3.4 gives the reader a roughly and
il-lustrative picture of the heterogeneous development that takes action in the combustion chamber when an injection is made.
When the injection is active the injected fuel is considered as an liquid column and travels into the liquid-zone. The injected fuel then atom-izes into small fine droplets and is entrained by the surrounding air. These droplets travel in a certain speed and are described by the fuel 2Intake Valve Closure
10 Chapter 3. The selected model
liquid prepared air burned
Figure 3.4: Illustrative picture of the jet formation.
spray submodel [2]. As the fuel evaporates and travels to the prepared-zone, air entrains and mix with evaporated fuel and then travels to the burned-zone. This means that mass flows between the zones. Figure 3.5 illustrate the only possible directions of the different mass flows over the zones.
Burned Liquid
Air Prepared
3.1. Model Structure 11
3.1.5 Initial conditions
There are a few initial conditions that must be defined before the simulation of the model can be started. The following table shows which variables and constants that must be initialized.
Constant name Description
pim Intake pressure at IVC
Tim Intake temperature at IVC
Tf uel Temperature on the fuel Twall Cylinder wall temperature
dn Nozzle diameter nrnozzles Number of nozzles
N Number of revolutions per minute
B Cylinder bore
a Crank radious
l Connecting rod length
prail Pressure in the common-rail pulsevector Vector with the injection profile
Chapter 4
Theory behind the models
This chapter presents the theory behind our implemented models.
4.1 Thermodynamic model
A thermodynamic model based on A DAE Formulation and it’s Numerical
So-lution for Multi-Zone thermodynamic models [13] is presented in this chapter.
The model is formulated as a differential algebraic equation model that is easy to transform numerically to a non-linear ordinary differential equation that can be solved. The resulting model gives the temperature and volume for each zone as well as the global pressure.
This multi-zone model is divided in the following zones: 1. Liquid
2. Air 3. Prepared 4. Burned
When the injection take place, the fuel jet forms a number of sprays, depend-ing on the number of injection nozzle holes. This liquid-zone is considered as a liquid following these assumptions [2]:
• Incompressible liquid.
• No heat transfer from the zone.
• The liquid only occupies a known volume of the combustion chamber.
For the air-, prepared- and burned-zone the following assumptions are made:
4.1. Thermodynamic model 13
• Uniform pressure into the combustion chamber at each time step. • The change in system volume and mass transfer between the zones are
known.
• Chemical equilibrium concentration in the burned zone. • Frozen state in air- and prepared zone, i.e no reactions.
• Mixture of ideal gas in each zone, with thermodynamic properties
de-pending on temperature, pressure and fuel-air ratio.
• Convective heat transfer for all zones. • Radiative heat transfer for burned zone. • No heat transfer between the zones.
In [13] a new approach in how to express and simplify the calculation of ther-modynamic process is presented. In this report two new expressions, well
stirred reactor and well stirred mixer, are introduced. The following
equa-tions are used to derive the expressions that describes a well stirred reactor and a well stirred mixer: There equation (4.1) describe the ideal gas law and equations (4.2) and (4.3) describes the energy in tha gas mixture.
pV = nRT (4.1) U = n(p, T, ¯xr) X i ˜ xi(p, T, ¯xi)˜ui(T ) or. (4.2) U = mX i xi(p, T, ¯xr)ui(T ) (4.3) xi= ˜ xiMi M (4.4)
there ¯xris the share of the respective atom among the reactants.
4.1.1 Implementation form of the equations
If the equations are studied for the well stirred mixer and the well stirred
re-actor -case it is shown that it is enough to implement the equation for well stirred reactor. The terms that differs between the two cases, for a gas that’s
not able to react, disappears when this equation form is used. It is therefore possible to conceal this information in the calculation of the different gas-properties. The full derivation from equations (4.1 − 4.4) to the equations implemented (4.5 − 4.7) can be further studied in appendix A2.
14 Chapter 4. Theory behind the models
In equations (4.1 − 4.4) there is only one zone considered with the same gas properties from source to destination. This is not adequate when simulating combusion with a multi-zone model since the gas must be able to flow from one zone with a specific ¯x to another zone and then get a new ¯x.
When a mass is transfered from one zone to another zone it could either mix or react with the existing gas depending on what type of zone it travels to (e.g. well stirred mixer or well stirred reactor). A gas that transfers to a well
stirred mixer is only mixed with the surrounding gas (e.g. no reactions at all).
If the same gas instead is transfered to a well stirred reactor it reacts with the surrounding gas. The mass transfer between the zones defines a system of type open. In figure 4.1 an open system with mass transfer is shown.
k2 ∆m k1 ∆m p,T ,dmk1 k1 p,T ,dmk2 k2 ∆Q ∆W p,T,V,m
In flows Out flows
Open system
Figure 4.1: Definition of directions for an open system. Meantime the period ∆t
flows the masselement ∆mjin over the systemboundary concurrently as the energy
∆Q leads in and the work ∆W performs on the controlvolume.
One important detail by using this approach is that there will be a straightfor-ward way to introduce the release of energy by using mass transfer between the zones in the equations. The entalphy, h(p, ˆTj, ˆ¯xr,j), that one mass
ele-ment brings to the new zone is not the same entalphy as if the mass eleele-ment would have originated from the same type of zone with the exact amount of energy that is released at the combustion. If the ˆx¯r,jthat includes entalphy in
the expression is the same as ¯xr,j, as in the source, then a mass transfer from well strirred mixer to well stirred reactor represents a combustion.
The equations that are needed and implemented are listed below.
p dV + µ V − m T ∂R ∂p ¶ dp−m µ R + T ∂R ∂T ¶ dT = ³ R+∇¯xrR· ¡ ˆ ¯ xr,d,j− ¯xr ¢´ T dmj (4.5)
4.2. Fuel injection model 15 m cvdT +m∂u ∂pdp+pdV = dQ+ ³ ∇x¯ru · (¯xr− ˆx¯r,s,j) + h(p, ˆTs,j, ˆ¯xr,d,j) − u ´ dmj (4.6) d¯xr=x¯r,d,j− ¯xr m dmj (4.7) Here are ˆ χd,j= ½
χj For flow from outside to inside (dmj> 0)
χ For flow from inside to outside (dmj ≤ 0) (4.8)
ˆ
χs,j=
½
f (χj) For flow from outside to inside (dmj> 0)
χ For flow from inside to outside (dmj≤ 0) (4.9) u = u(p, T, ¯xr) = X k xk(p, T, ¯xr) uk(T ) (4.10) For χ ∈ {T, ¯xr, xk}. a01 1p b01 c1 p d1 dVdp1 dT1 = dV ³ R + ∇¯xrR · ¡ ˆ ¯ xr,d,j− ¯xr ¢´ T dmj dQ +³∇¯xru · (¯xr− ˆx¯r,d,j) + h(p, ˆTd,j, ˆ¯xr,s,j) − u ´ dmj (4.11) there ai = V − m T ∂R ∂p bi = −m µ R + T ∂R ∂T ¶ ci = m∂u ∂p di = m cv
4.2 Fuel injection model
The figure 4.2 shows which signals that are sent into the submodel and what signals that comes out from the submodel.
Fuel Injection Submodel
p,_cyl, P_rail, N m_f, u
Figure 4.2: In- and outsignals from the model
16 Chapter 4. Theory behind the models
implemented in the total model. The timing and rate of fuel injection affect the spray dynamics and combustion characteristics. If the pressure upstream of the injector nozzle can be measured or estimated and assuming the flow through each nozzle is quasi-steady, incompressible, and one dimensional, the mass flow rate of fuel through the nozzle,mf,inj˙ , is given by:
˙
mf,inj = CDAN
p
2ρl∆p (4.12)
where AN is the nozzle minimum area, CDthe discharge coefficient, ρ the
density of liquid fuel, and ∆P the pressure drop across the nozzle. [1] Since ˙mf,inj = ANρlui, the fuel injection velocity at the nozzle tip ui, can
be expressed as:
ui= CD
s 2∆p
ρl (4.13)
The discharge coefficient, CD, have been investigated by [2] for several
en-gine operating condition. As a result of their correlation analyses, the best compromise between accuracy and generalization for CDis to use a function
depending on the volume injected fuel qf ueland engine speed N .
CD= a1− a2· (qf uel· N ) if (qf uel· N ) ≥ 1 − a1 a2
CD= 1 if (qf uel· N ) ≤ 1 − a1 a2
(4.14)
Here a1= 1.1774, a2= 3.95 · 10−6, N is the engine speed in rpm and qf uel
is the volume injected in mm3. [2]
4.3 Fuel spray
At the start of injection, fuel begins to penetrate into the combustion chamber and high temperature air is entrained into the spray. The hot air evaporates the fuel and beyond a fixed length, known as the break-up length, no liquid fuel exists. The liquid length shortens slightly after the start of combustion but remains relatively constant until the end of injection. Beyond the break-up length, the rich premixed fuel and air continue to be heated until they react in the rich premixed reaction zone.[8]
Figure 4.3 shows an general overview of the fuel spray and its flame prop-agation. The products of rich combustion continue downstream and diffuse and mix radially outward until reaching the surrounding cylinder gases. At a location where the rich products and cylinder gases mix to produce a stoichio-metric mixture, a diffusion flame is produced. The diffusion flame surrounds the jet in a thin turbulent sheet, which extends upstream toward the nozzle.
4.3. Fuel spray 17
Figure 4.3: General view of an quasi-steady diesel combustion plume [8].
Soot is burned out and N Oxis produced on the outside of the diffusion flame,
where temperatures are high and oxygen and nitrogen are abundant.[8] Figure 4.4 shows the liquid phase and vapour phase of dme1 in different
Figure 4.4: How liquid and vapour phase propagates in time.
conditions and how they propagates in time. The rail pressure was set to 400 bar and the injection duration was 3 ms. This figure shows in a distinct way the fuel spray behaviour with both liquid and vapour phase. [12]
4.3.1 Fuel spray submodel
Figure 4.5 shows which signals that are sent into the submodel and what sig-nals that comes out from the submodel.
18 Chapter 4. Theory behind the models
Fuel Spray Submodel p_cyl, p_rail,
t_inj_start, N m_ae
Figure 4.5: In- and outsignals from the fuel spray submodel
The fuel spray submodel describes the fuel motion from the nozzle hole into the combustion chamber. In every time step the model predicts the spray tip penetration ssprayand the spray velocity Uspray. It also predicts the mass of
the entrained air ma,einto the fuel spray.
The injected fuel is assumed to be a liquid column that is connected to the liquid-zone. The liquid column travels through the nozzle hole exit at a con-stant velocity U0 into the cylinder before the fuel spray breakup time, tb,
occurs. This relation is given by the following equations:
U0= CD s 2∆p ρl (4.15) tb= 4.351 ρl· dn C2 D √ ρa∆p (4.16) Where CDis the discharge coefficient of the fuel injector, ∆p is the pressure
drop through the nozzle hole given in [P a], dnis the nozzle hole diameter in
[mm], ρlis the density of the fuel and ρais the air density in the air-zone.
After the break-up time, t ≥ tb, the fuel is assumed to be atomized into fine
droplets. Then there will be a descending velocity of the fuel spray, Uspray:
Uspray = 2.95 2 µ ∆p ρa ¶1 4rd n t (4.17)
To get the fuel spray break-up length, sb, and the spray tip penetration sspray
are the two equations (4.15) and (4.17) integrated. The break-up length is defined as the length where the fuel spray liquid column atomizes into fine droplets and the spray tip penetration is the total length of the fuel spray that reaches into the combustion chamber. The equations for fuel break-up length and spray tip penetration is given by:
sb(0 < t < tb) = U0· t = CD s 2∆p ρl · t (4.18) sspray(t ≥ tb) = 2.95 2 µ ∆p ρa ¶1 4p dn· t (4.19)
The mass of the entrained air, ma,eis described by the rate of air that entrains
4.4. Fuel evaporation submodel 19
the conservation of the momentum the prediction of the entrained air can be described by the following equation:
˙ ma,e= − Rt 0m˙f,inj(t) dt · U0 (Uspray(t))2 · ˙Uspray(t) (4.20)
Where mf,inj is the mass of the injected fuel. The integral describes the
cumulative fuel mass injected and ˙Uspray is the gradient of the fuel spray
velocity. For a more detailed description see appendix A1. [4], [2]
4.4 Fuel evaporation submodel
Figure 4.6 shows which signals that are sent into the submodel and what signals that comes out from the submodel. The evaporation submodel
de-Fuel Evaporation Submodel
p_O2, m_f_inj m_fp
Figure 4.6: In- and outsignals from the fuel evaporation submodel
scribes the evaporation process with a semi-empirical model proposed by Whitehouse and Way [3]. With this model approach some precision is lost due to the fact that the fuel atomization and vaporization are neglected. Fuel prepared-rate is only considered in this model.
The fuel is prepared after it has atomized and evaporated and then micro-mixed with the entrained air. The prepared mass flow is depending on the injected fuel at that time, on the entrained air (partial oxygen pressure in the prepared-zone) as well on the amount of fuel that is injected but not yet pre-pared. Following equation gives the relation between these dependencies:
˙ mf,p(t) = C1·180ω π · µZ t 0 ˙ mf,inj(t) dt ¶1 3 (pO2(t))0.4· · µZ t 0 ˙ mf,inj(t) dt − Z t 0 ˙ mf,p(t) dt ¶2 3 (4.21)
where ω is engine speed in£rad s
¤
, pO2is the partial oxygen pressure in the
air-zone in [bar] and C1is a constant assumed equal to 0.035
h bar−0.4 deg i . [2], [3]
4.5 Combustion submodel
Figure 4.7 shows which signals that are sent into the submodel and what sig-nals that comes out from the submodel. The combustion submodel also uses
20 Chapter 4. Theory behind the models
Fuel Combustion Submodel
p_O2, T_mean, m_fp m_fb
Figure 4.7: In- and outsignals from the combustion submodel
an semi-empirical model that is strongly connected to the fuel evaporation submodel. The mass of the burned fuel, mf,b is predicted by this model.
There are two equations describing the rate of combustion. First is the rate of combustion, ˙mf,b, and the second is the mean gas temperature of the three
zones. ˙ mf,b(t) = C2· pO2 N0 ·pTmean(t) · 180ω π · e ³ −T (t)TA ´Z t 0 ( ˙mf,p(t) − ˙mf,b(t)) dt (4.22) Tmean(t) = P kPTi(t) · mi(t) kmi(t) (4.23)
Here ω is the engine speed in£rad s
¤
, pO2is the partial oxygen pressure of the
air-zone in [bar], N0is the engine speed in [rps]. C
2and TAis assumed to
be equal to 1.2 · 1010hK0.5 bars
i
and 16500 [K]. Tiand miare the temperature
and mass for the zone i = a, p, b.[2]
In the early stages of combustion the preparation rate, ˙mf,p, is greater than
the burning rate, ˙mf,b, and with an accumulation of prepared fuel it results
in a premixed combustion process. When the energy of the premixed com-bustion comes to an end, the evaporation and comcom-bustion rates are equal and resulting in a mixing-controlled combustion process [3].
4.6 Heat transfer submodel
Figure 4.8 shows which signals that are sent into the submodel and what signals that comes out from the submodel. Two types of heat transfer are
Thermodynamic Submodel
p, T, m, phi dp, dT, dphi
Figure 4.8: In- and outsignals from the heat transfer submodel
discussed in this model; convective heat transfer and radiative heat transfer. The most part of the heat transfer in internal combustion engines comes from convection. This is when heat is transfered through fluids in motion or a fluid and solid surface in relative motion. The forced convection is used when the motions are produced by forces other than gravity. In this case there is forced
4.6. Heat transfer submodel 21
convection between the in-cylinder gases and the cylinder head, valves, cylin-der walls and piston during the different phases. The heat transfer caused by radiation occurs from the high temperature combustion gases and hot parti-cles in the flame region to the combustion chamber walls. The concept of heat transfer by radiation is based on the emission and absoption of electro-magnetic waves.[1]
In the burned-zone there are both convective and radiative heat transfer. The total heat transfer in the burned-zone is calculated by the sum as follow:
˙
Q = ˙Qc+ ˙Qr (4.24)
The convective heat transfer is described by Newons law of cooling: ˙
Qc= hcA (T − Tw) Cc (4.25)
Here T is the temperature in the zone, Tw is the in-cylinder wall
tempera-ture, Ccis calibration parameter, A is the in-cylinder area and hcis given by
Woschnis correlation as:
hc = 0.013 ·
p0.8³C
1up+ C2(p−pprmV)TrrV
´0.8
B0.2· T0.55 (4.26)
Here the constants are set to C1= 2.28 and C2= 0 during the
compression-phase. During the combustion-phase the constants are set as C1 = 2.28 and
C2 = 3.24 · 10−3. The other constants and parameters can be seen in table
4.6.
Constant Description Unit
up Mean piston speed ms
B Cylinder bore [m] T Temperature [K] pr Reference pressure [Pa] Vr Reference volume [m3] Tr Reference Temperature [K] p Fired pressure [Pa] p0 Motored pressure [Pa] C1 Constant [−] C2 Constant [sKm]
The radiative heat transfer is described by using Stefan-Boltzmann law: ˙ Qr= σA ¡ T4 b − Tw4 ¢ Cr (4.27)
Where σ is Stefan-Boltzmanns constant, Cris a calibration parameter and Tb
Chapter 5
Implementation
This chapter will describe how the model was implemented into the Mat-lab/Simulink environment. Matlab is a numerical computing environment but also a programming language. Simulink is a tool in Matlab for modeling, simulating and analyzing dynamic systems.
5.1 General view
The entire model consists of all submodels presented in previous chapter and these submodels are implemented in Simulink and a few as S-functions. To simplify the work to implement our multi-zone model has a package called psPack1 been used. Further information about psPack is presented in
sec-tion 5.5. The submodels that have been implemented in Simulink contains information that are used by the S-functions2that handles compression and
combustion.
5.2 Simulink
Simulink is the environment where all the submodels, presented in the Model theory chapter, was put together to a working unit. Below, in figure 5.1, an example is shown on how the implementation in our model is made, in this case the fuel spray submodel. To the left in the figure is the submodel com-municating with all other submodels presented (the top layer). The right part of the figure shows how the fuel spray submodel is built with more submodels that represents different equations (4.15, 4.16, 4.17) in the model.
1Engine simulation tool developed at Vehicular systems at LiTH 2Internal function in simulink, often written in C- code
5.3. S-functions 23 Fuel Spray after_break_up Goto24 m_dot_ae Goto23 p_rail p_cyl fuel_injected t_inj,start air_density burn_completed C_D m_dot_a,e after break-up
Fuel Spray Submodel [C_D] From65 [air_density] From6 [fuel_injected_part] From44 [t_inj_start] From43 [comb_enable] From39 [p_cyl] From36 [burn_completed] From33 -C-0:0 Constant4 2 after break-up 1 m_dot_a,e Product m_finj U_0 U_ab m_dot_a,e Equation_22 p_rail p_cyl t_inj,start air_density U_ab Equation_20 p_rail p_cyl C_D air_density t_b Equation_19 p_rail p_cyl C_D U_0 Equation_18 t_b t_inj,start after_break-up before_break-up Break-up length Enable 7 C_D 6 burn_completed 5 air_density 4 t_inj,start 3 fuel_injected 2 p_cyl 1 p_rail
Figure 5.1: A general view of the model to demonstrate how the model is implemented
with the different layers in simulink.
5.3 S-functions
In the final model several S-functions have been used. These have been coded in the m-language and are implemented as Level 2 M-file S-Functions. The main S-functions are those who handles the compression and combustion. These S-functions calculates the thermal properties, pressure, temperatures and volumes for the different zones. Some of this information is then feeded back to submodels. There are also S-functions that handles the fuel injection system.
5.4 Solver
To solve the differential equations is a stiff ode3 solver used. The problem
is stiff if the solution being sought is varying slowly, but there exists nearby solutions that vary rapidly, so the numerical method must take small steps to obtain satisfactory results.
5.5 psPack
This is a simulation tool that initally was designed for simulation of SI-engines. This package has been stripped down and only the necessary func-tions are used. In the psPack-menu changes can be made in a few engine parameters such as geometry and engine speed. psPack is allso used to calcu-late thermal properties for the burned gas. It uses a table where it is looking up the desired thermal property for the current pressure p, temperature T and mass fraction of fuel and air in the zone. This package is developed for Mat-lab/Simulink.
24 Chapter 5. Implementation
5.5.1 Thermal Properties
To calculate the desired thermal property some arguments are sent to the psPack function, psThermProp, that is needed to interpolate in the tables. As mentioned above it needs p, T and mass fraction of fuel and air for the specific zone. To simplify the call of the thermal property function4the mass
fraction are divided as a vector Xgcthat consists of the fraction of unburned
and burned mass of fuel and air. It can be seen in equation 5.1:
Xgc=
¡
xf,u xa,u xf,b xa,b
¢
(5.1) where xf,uand xa,ustands for the mass fraction in an unburned zone and xf,b
and xa,bstands for the same in the burned zone. In our setup of zones there are
an air-zone, prepared-zone and a burned-zone. The air-zone is considered as air that is unburned and the prepared-zone is considered as vaporized fuel that also is unburned. In the burned-zone air and vaporized fuel have reacted and there is a mixture of burned fuel and air. Initially there exists a small fraction of burned fuel and air due to residual gas from previously combustion. In equation 5.2 it is shown what the setup of the zones looks like.
Xgc= XXgc,agc,p Xgc,b = x0f,u xa,u0 00 00 0 0 xf,b xa,b (5.2)
where row one is the air-zone, row two is the prepared-zone and row three is the burned-zone.
Chapter 6
Validation
In this chapter the validation steps is presented. Validation of the submodels have been carried out in two steps. Both when the submodels are separate units and when they have been put togehther to one unit.
6.1 Comments about the Validation
The important content of the model is that it should predict torque in a correct way. Unfortunately it is not possible to validate the total model in an good way because the lack of engine measurement data. Although validations of some of the submodels are presented in this chapter. When validations are not possible, experiments have been performed to show that the submodels probably act as it supposed to. With the measurement data thats available can the different submodels behavior be studied in detail. If the submodels behavior is concurrent with the measurement it is probably a good indication that the total model also will concur.
6.2 Fuel injection
The fuel injection is described, as equation (4.12), and is very dependent of the amount of fuel injected hence the parameter CD change as equation
(4.14). A test was formed to show how the parameter CD affects the mass
flow rate at the injection. The test setup can be seen in table 6.1. Figure 6.1 shows the control signal, for the different cases, plotted in the same figure as fuel mass flow rate. As the injected mass increases the parameter CD
changes. These phenomena can be seen as when the first part of the fuel is injected it does not encounter any major resistance. When the amount of fuel increases in the cylinder the later part of the injected fuel encounters a resistance so that it bumps into the aldready injected fuel and therefore slows
26 Chapter 6. Validation
Injection law set nr Rail pressure Injected fuel N
1 800 [bar] 32.9 [mg] 2500 [rpm]
1 1000 [bar] 36.4 [mg] 2500 [rpm]
1 1200 [bar] 39.4 [mg] 2500 [rpm]
Table 6.1: Table of fuel injection test setup
down the fuel mass flow rate. The resistance that is increased comes from the model of CDthat is described by equation (4.14).
−15 −10 −5 0 5 10 15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Injection control signal and injected fuel mass flow
Control signal theta [deg] −15 −10 −5 0 5 10 150 0.01 0.02 0.03 0.04 0.05 0.06
Fuel mass flow [kg/s]
800 bar 1000 bar 1200 bar
Figure 6.1: Fuel injection control signal and mass flow rate that shows the changes in
CDfor different injection pressures. The decrease in CDcan be seen in the decrease
of the mass flow after about 2 deg.
6.3 Fuel spray validation
To validate the spray penetration correlation, experimental data collected by Dan et al. [9] were compared with the implemented model predictions. The injection conditions and ambient conditions of the experiment are summa-rized in Table 6.2 The injector nozzle has a mini-sac volume design for high injection pressure. The injection pressure was varied from 55 MPa to 120 MPa. In figure 6.2 and 6.3 simulations are compared to the measurements of the spray tip penetration as a function of time from start of injection and injection pressure.
In figure 6.2, the measured spray penetration for an injection pressure of 120 MPa is compared with the simulated data from the model. It shows that the implemented model over predicts the spray tip penetration. When the injec-tion pressure is lower, in this case 55 MPa, the model has a better accuracy
6.3. Fuel spray validation 27
Parameter value/spec
Hole diameter [mm] 0.2
Hole length [mm] 1.1
Number of holes [-] 1
Discharge coefficient of the hole [-] 0.66 Injection pressure [MPa] 55, 120
Ambient pressure [MPa] 1.5
Ambient temperature [K] 293 Ambient density [mkg3] 17.3
Ambient viscosity [·10−6P a · s] 17.5
Table 6.2: Experimental setup for the fuel spray validation.
but it still over predicts. This result can be seen in figure 6.3 . This over-prediction probably comes from the disregard of the ambient viscosity in our model that is used in the experimental setup.
0 0.5 1 1.5 2 2.5 x 10−3 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Injection with a rail−pressure at 120 MPa
Time after injection [s]
Spray tip penetration [m]
Simulation Experimental
Figure 6.2: Spray tip penetration as function of time with fuel injection pressure 120
MPa. As can be seen the model overpredicts the penetration length slightly.
In figure 6.4 it is shown how the length of the spray tip varies with different sets of rail-pressure. The liquid length is the fuel spray break-up length and is shown as the solid line in the figure. The length of the dropplet based spray is the dotted length and the total fuel spray penetration length is the solid and dotted line together. In this simulation was a simulation time of 1.4 millisecond used and the rail pressure was in the four cases 60, 80, 100, 120 MPa.
28 Chapter 6. Validation 0 0.5 1 1.5 2 2.5 x 10−3 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Injection with a rail−pressure at 55 MPa
Time after injection [s]
Spray tip penetration [m]
Simulation Experimental
Figure 6.3: Spray tip penetration as function of time with fuel injection pressure 55
MPa. Here it also shown that the model sligthly overpredict the penetration length.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1
2 3 4
Spray tip penetration [m]
Test Nr:
Length of spray tip
Figure 6.4: Spray tip length, for different injection pressures. From the top: 120, 100,
80, 60 MPa The solid line represents liquid length. As expected the penetration is larger for higher pressures.
6.4 Fuel evaporation model
To validate the fuel evaporation model the injected fuel mass and the mass of the evaporated fuel are plotted in the same plot. Figure 6.5 shows the injection and evaporation of fuel with only a main injection. It is shown that the evaporation process looks like a first order system and this seems to be correct when a comparison are made between these plots and the plots presented in the Salerno rapport [2]. In figure 6.6 is a new simulation made with the difference that both pre- and main injection is used.
6.4. Fuel evaporation model 29 0.0230 0.0235 0.024 0.0245 0.025 0.0255 0.026 0.5 1 1.5 2 2.5 3 3.5 4x 10
−5 Injected and evaporated fuel (Injection law nr:1 )
Time [s]
Mass [kg]
Fuel mass injected Fuel mass evaporated
Figure 6.5: Fuel injection and evaporation, main injection (injection law nr 1). The
shape of the evaporated mass is consistent with a first order system and the result is similar to the result in [2].
0.02250 0.023 0.0235 0.024 0.0245 0.025 0.0255 0.026 0.5 1 1.5 2 2.5 3 3.5 4 4.5x 10
−5 Injected and evaporated fuel (Injection law nr:2 )
Time [s]
Mass [kg]
Fuel mass injected Fuel mass evaporated
Figure 6.6: Fuel injection and evaporation, pre + main injection (injection law nr 2).
When using multiple injections the evaporated mass is still consistent with a first order system.
In the following figure it’s presented how the rate of evaporation varies during the injection. In figure 6.7 the rate for both injection law one and two is plotted, see Table 6.5 for more information.
30 Chapter 6. Validation 0.02250 0.023 0.0235 0.024 0.0245 0.025 0.0255 0.026 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Fuel evaporation rate (Injection law nr: 1 & 2 )
Time [s]
Massrate [kg/s]
Injection law 1 Injection law 2
Figure 6.7: Fuel evaporation rate for injection law nr 1 plotted with injection law 2.
This shows how the fuel evaporation rate varies during two different types of injec-tions.
6.5 Evaporation and combustion submodel
In the model the atomization of fuel into droplets, vaporization of the fuel, entrainment of air and micromixing of fuel and air are joint together and is known as preparation of fuel according to the equations (4.21,4.22). At the start of the combustion the fuel burning rate is lower than the preparation rate. As the prepared fuel is accumulated it causes an increase in the burning rate. Then, as the combustion proceeds, the burning rate increases faster than the preparation rate. When the prepared fuel is depleted the burning rate is de-creasing. This is a result of premixed combustion process and the burning rate is controlled by the chemical kinetics.[3]
To validate the premixing combustion process a test setup in table 6.3 was used.
Start of injection Fuel injected
θ = 4.76 deg BT DC 21.56 [mg]
Table 6.3: Test setup for evaporatin and combustion validation.
In figure 6.8 it’s shown that this premixed behaviour starts at 4 [deg] BTDC and ends at 4 [deg] ATDC. After the premixed behaviour is completed the mixing controlled combustion starts. As a result of the mixing controlled combustion process the combustion and preparation rate keeps equal to the
6.5. Evaporation and combustion submodel 31
end of the combustion. In the same figure it can be seen that the mixing con-trolled combustion process proceed after 4 [deg] ATDC and ending at 27 [deg] ATDC. 0 5 10 15 20 0 2 4 6 8 10 12
x 10−3 Prepared and burn rate
theta [deg]
Mass rate [kg/s]
Prepared fuel rate Burned fuel rate
Figure 6.8: Mass flow rate for prepared-zone and combustion-zone. The premixed
behaviour can be seen between 4 BTDC and 4 ATDC. After that the mixing controlled combustion starts. 0 5 10 15 20 25 0 0.5 1 1.5 2
x 10−5 Prepared and burned mass
theta [deg]
Mass rate [kg]
Prepared fuel mass Burned fuel mass
Figure 6.9: Inserted mass for prepared and combusted fuel. As seen in figure the shape
of the cumbusted fuel is consistent with a first order system.
In figure 6.9 it is shown that the prepared mass and burned mass behave like a first order system. The equations (4.21) and (4.22) prove that this is a correct behavior. In equation (4.22) it is clear that the early stages in the combustion
32 Chapter 6. Validation
is controlled by an Arrhenius1 like part. This part describes the
tempera-ture dependece of the rate of chemical reaction. It can also be considered to represent the ignition delay time. The constant C2also controls the ignition
delay time. In the simulation of the burning rate is the end of combustion considered as when the burned fuel fraction reaches 0.9995, as described in equation (6.1):
mf,b
mf,inj ≥ 0.9995 (6.1)
6.6 Heat transfer model
In this section the implemented heat transfer model is validated. In table 6.3 the setup for this validation is presented. Figure 6.10 shows how the convective and radiative heat transfer varies during the cumbustion process. Lack of validation data will force to validate the model just by looking at the fundamental appearance of the heat transfer curves. The figure also shows that the convective heat transfer stands for the largest part of the total heat transfer. When the combustion starts, just before TDC, the radiative heat transfer increases, and is at most about 30 percent of the total heat transfer.
−600 −40 −20 0 20 40 60 80 100 2000 4000 6000 8000 10000 12000 14000 Heat transfer theta [deg] dQ [W/(m 2 K)]
Convective heat transfer Radiative heat transfer Total heat transfer
Figure 6.10: Total heat transfer for a simulation. In figure it is show that the largest
part for the heat transfer originates from convective heat transfer.
1The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature
6.7. Thermal properties 33
6.7 Thermal properties
One important part of model accuracy is to have correct values for the thermal properties of the different zones. There exist a program called Chepp2which
calculates the thermal properties for differents types of zones. Unfortunately this program could not be used in the final product. Tables are used as a re-placement to obtain the desired thermal property for the specific mass fraction of air and fuel (xf,u, xa,u, xf,b, xa,b), T and p. If some value is going out of
bound the tables extrapolates.
In figure 6.11 6.12 6.13 it is shown that the table calculations fit the cal-culations produced from Chepp. These calcal-culations have been made for an unburned zone where xf vary from 0 to 1. To to get a clearer view the
calcu-lations for the tables have been downsampled.
0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6x 10 5 Enthalpy, h xf h [J/kg] Chepp Tables
Figure 6.11: Comparsion between Chepp and tables for calculation of enthalpy. It is
shown that the values from generated from tables correspond very well to the values produced from Chepp.
6.8 Heat release analysis
In this section two experiment are made to validate the heat release. The heat release rate for the experiment is given by real measurments from GM. The heat release for the simulated model is approximated with the fuel burn rate e.g. ˙mf b. In table 6.4 the model parameters that is used in the simulation is
presented.
34 Chapter 6. Validation 0 0.2 0.4 0.6 0.8 1 50 100 150 200 250 300 Gas constant, R x f R [J/kg K] Chepp Tables
Figure 6.12: Comparsion between Chepp and tables for calculation of the gas
con-stant. As seen in figure 6.11 the values from tables in this figure correspond very well to values from Chepp.
0 0.2 0.4 0.6 0.8 1 400 500 600 700 800 900 1000 1100 1200
Specific heat constant at constant pressure, cp
xf cp
[J/kg K]
Chepp Tables
Figure 6.13: Comparsion between Chepp and tables for calculation of cp. As figure 6.11 and 6.12 the values from tables in this figure correspond very well to values from Chepp.
In figure 6.14 and 6.15 the heat release rate from experimental data versus the simulated burn rate is presented. In the figures are the levels matched just to get a good appearance because the interest is only when the peaks occurs. The highest peak in figure 6.14 and 6.15 for the heat release rate starts just before TDC and is also the same for the burn rate.
The model parameter TA has been set to 20500 to match the experimental
data. In figure 6.16 a sensitivity analysis is shown, were the parameter TA
6.8. Heat release analysis 35
Variable Value Unit
Tim 325 [K]
Tres 440,480 [K]
xres 33 [%]
TA 20500 [K]
Table 6.4: Setup for heat release experiment one and two.
−400 −30 −20 −10 0 10 20 30 40 20 40 60 80 100 120 140 160 180 200 θ [deg] Heat release vs burned rate
Heat release from experiment Burned rate from simulation
Figure 6.14: Heat release for experiment one. As can be seen in figure the timing of
heat release and the burned-rate is matched good, around TDC.
−400 −30 −20 −10 0 10 20 30 40 20 40 60 80 100 120 140 160 180 200 θ [deg] Heat release vs burned rate Heat release from experiment Burned rate from simulation
Figure 6.15: Heat release for experiment two. As can be seen in figure the timing of
heat release and the burned-rate is matched good, around TDC.
for experimental data two is located in Appendix B. It shows that an increase in the parameter TApostpone the first burn rate peak and a decrease in the
36 Chapter 6. Validation
same parameter moves the first burn rate peak earlier. The position of the main peak is not affected of changes in TA. This is because that the
com-bustion already has started and when the second injection occurs it ignites at once. This means that evaporation rate and combustion rate is the same after the first injection.
An sensitivity analysis has also been performed in the parameter Tres. The
parameter varies with ±10% and the figures are located in Appendix B.
−400 −30 −20 −10 0 10 20 30 0.005 0.01 0.015 0.02 0.025 0.03 θ [deg] Burn rate Burn rate TA = 20500 TA = 22550 TA = 18450
Figure 6.16: Burnrate for different TA in experiment two. Experminet varies with
±10% in the parameter and shows that the first peak can be placed further from or
closer to the main injection.
6.9 Pressure
Figure 6.17 and 7.1 shows the pressure trace from our model compared with experimental data number one. In figure 6.17 it shows that the model predicts the pressure in a good way. However the top pressure is over estimated with about 5 bar.
In figure 6.18 the pressure trace from experimental data two is compared with the simulated model. In this work point3 the top pressure is even more
over estimated and the first pressure top that occurs at TDC is heavily under estimated. This is shown in figure 6.18.
6.10. In-cylinder temperature 37 −300 −200 −100 0 100 200 300 0 20 40 60 80 100 120 140 Cylinder pressure θ [deg] Pressure [bar] Experimental pressure Simulated pressure
Figure 6.17: Pressure-trace for experiment one. It is shown that the simulated pressure
is slightly under predicted at TDC and slightly over predicted a few degrees after TDC.
−300 −200 −100 0 100 200 300 0 20 40 60 80 100 120 140 Cylinder pressure θ [deg] Pressure [bar] Experimental pressure Simulated pressure
Figure 6.18: Pressure-trace for experimental setup two. The under and over prediction
of the simulated pressure is a bit larger than seen in figure 6.17.
6.10 In-cylinder temperature
To show the effects of pre-injection a test set was constructed, see table 6.5. In figure 6.19 the temperature in the burned-zone is plotted against the crank angle, evidencing an minor increase of the maximum temperature in the test case with only one main injection. In the presence of pre and main injection, test case 2, the maximum temperature is reduced. This reduction is achieved due to the reduced mass of fuel of the main injection, although the same amount of injected fuel is the same in both test cases.
38 Chapter 6. Validation
Injection type Inj 1 Inj 2
Only main
-n
θstart=7 deg BT DC
minj=15.37[mg]
o
Pre- and main n θstart=25.7 deg BT DC minj1=2.76[mg] o n θstart=7 deg BT DC minj2=12.65[mg] o
Table 6.5: Table of injection law sets. The two different injections has the same total amount of injected fuel.
0 5 10 15 20 25 30 1800 1900 2000 2100 2200 2300 2400 2500
Temperature in burned zone
θ [deg]
Temperature [K]
Main injection Pre− and main injection
Figure 6.19: Difference between temperature in the burned zone. It is shown that a
injection law with pre + main injection may reduce the high temperature.
The IMEP4is almost the same for the two cases (14.12, 14.5) bar. This is
ev-idencing that the occurrence of pre-injection may reduce the maximum tem-perature while keeping almost the same IMEP, with benfits of lower N Ox
emissions. These is the same conclusions that is made in (Arise et al., 2005) [2].
